Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.QuasiCompact
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism is "quasi-compact" if the underlying map of topological spaces is, i.e. if the preimages of quasi-compact open sets are quasi-compact.
- Cited by
- 102 results in Mathlib
- Foundations
- Depth 99 from the axioms, rests on 1,346 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by116
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.normalizationstatement and proof · cited by 41
- AlgebraicGeometry.Scheme.Hom.toNormalizationstatement and proof · cited by 28
- AlgebraicGeometry.Scheme.Hom.fromNormalizationstatement and proof · cited by 28
- AlgebraicGeometry.Scheme.Hom.normalizationCoprodIsostatement and proof · cited by 15
- AlgebraicGeometry.Scheme.Hom.ker_applystatement and proof · cited by 14
- AlgebraicGeometry.Scheme.Hom.normalizationDescstatement and proof · cited by 10
- AlgebraicGeometry.Scheme.Hom.normalizationOpenCoverstatement and proof · cited by 9
- AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpacestatement and proof · cited by 7
- AlgebraicGeometry.Scheme.Hom.support_kerstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalizationstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.normalizationObjIsostatement and proof · cited by 6
- AlgebraicGeometry.QuasiCompact.isCompact_preimagestatement and proof · cited by 5